Problem: Dots are spaced one unit part, horizontally and vertically. What is the number of square units enclosed by the polygon?
[asy]
/* AMC8 1998 #6P */
size(1inch,1inch);
pair a=(0,0), b=(10,0), c=(20,0), d=(30, 0);
pair e=(0,10), f=(10,10), g=(20,10), h=(30,10);
pair i=(0,20), j=(10,20), k=(20,20), l=(30,20);
pair m=(0,30), n=(10,30), o=(20,30), p=(30,30);
dot(a);
dot(b);
dot(c);
dot(d);
dot(e);
dot(f);
dot(g);
dot(h);
dot(i);
dot(j);
dot(k);
dot(l);
dot(m);
dot(n);
dot(o);
dot(p);
draw(a--b--g--c--d--h--l--k--o--j--i--e--a);
[/asy]
Answer: Slide triangle $A$ down to fill in triangle $B$. The resulting $2\times 3$ rectangle has area $\boxed{6}$. [asy]
/* AMC8 1998 #6S */
size(1inch,1inch);
pair a=(0,0), b=(10,0), c=(20,0), d=(30, 0);
pair e=(0,10), f=(10,10), g=(20,10), h=(30,10);
pair i=(0,20), j=(10,20), k=(20,20), l=(30,20);
pair m=(0,30), n=(10,30), o=(20,30), p=(30,30);
dot(a);
dot(b);
dot(c);
dot(d);
dot(e);
dot(f);
dot(g);
dot(h);
dot(i);
dot(j);
dot(k);
dot(l);
dot(m);
dot(n);
dot(o);
dot(p);
draw(a--b--g--c--d--h--l--k--o--j--i--e--a);
pen p = linetype("4 4");
draw(b--c, p);
draw(j--k, p);
label("A", k, NW);
label("B", c, NW);
[/asy]